The new, smaller plants remain on the main stump which has been cut... Yes, they might 'only' maje small versions of the original plant, but this will depend on the plant's position and nutriment: enriching the soil, mulching heavily, or great positioning amongst other symbiotic plants will allow new growth to flourish significantly.. Double-digging and creating mounds can help with this: here's a book that I highly recommend to study if you can (you may find it in PDF form online):